I helped my mother and my aunt clear my grandmother's house when she went into a home. She was not there for the clearance. I think that things that might be handed down later, and personal papers, went into storage. We mostly focused on clothes (what would she need in the home, and what wouldn't she wear again), and I guess things like plants and kitchen equipment/food that wasn't going to be needed again. I remember emotions ran high.
I think the idea of lots of lidded boxes and labels is a good one. Transparent lidded boxes are best, and label them on several sides and on the top, so you can see the contents however they end up being stored. The reminder to look in all pockets of clothes before donating is also good!
I agree that giving a charity first choice of things that the family is not going to keep could be a good way to cut down on you having to dispose of things.
If it's the kind of house where there are lots of books, would it make sense to give a local bookseller first refusal before bringing in the charity shop?
If it's the kind of area where people leave stuff out on the pavement to be collected, might it be worth doing this or using Olio with some of the stuff to cut down on disposal costs? Of course, it takes more time to do it that way.
Wishing you and your family good luck with it.